Abstract
A generalization of the direct method of Clarkson and Kruskal for fiuding similarity reluctions of a PDE is found and discussed. The generalization incorporates the singular manifold method largely based upon the Painlevé property. The symmetries found in this way are shown to be those corresponding to the so-called nonclassical symmetries by Blumen and Cole and Olver and Rosenau. The procedure is applied to the Burgers equation.
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Additional information
Area de Fisica Teorica, Facultad de Ciencias Universidad de Salamanca, 37008 Salamanca, Spain. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 250–256, May, 1994.
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Estevez, P.G., Gordoa, P.R. Nonclassical symmetries and the singular manifold method: The Burgers equation. Theor Math Phys 99, 562–566 (1994). https://doi.org/10.1007/BF01016139
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DOI: https://doi.org/10.1007/BF01016139